On Some Solutions of Kawahara and Modified Kawahara Eqautions

Abstract

The study introduces the Quantum-Inspired Real-Time Decomposition Method (Q-RDM) in the shape of a new calculation tool that can be applied to solve the complicated mathe- matical model according to the Fractional Kawahara and Modified Kawahara equations. The plasmas and shallow water behavior of waves are explained with the help of the equations and the traditional approaches are not able to explain this properly due to the high computational cost and the numerical instability. Q-RDM offers the answer to these problems through a better way to optimize the classical Adomian Decomposition Method through a clever and adaptive optimization loop that uses quantum control theory. This al- lows the algorithm to self-correct in real-time stabilizing the answer without even needing complex linearization. As our results have demonstrated, Q-RDM is not just a much faster means of obtaining a 56 fold minimum reduction in processing time compared to current algorithms but is also a much more accurate technique since it was able to deal with errors in calculations that plague the traditional algorithms.